Introduction
Profit, Loss and Discount is one of the highest-frequency arithmetic topics in every Bangladeshi competitive exam — BCS Preliminary, Bank (Senior/Officer, Cash), and IT-officer written and MCQ papers. Almost every exam sets at least one or two questions from it, and the same ideas reappear inside data-sufficiency, word problems, and even simple interest questions.
The topic is purely about buying and selling: how much you paid, how much you sold for, whether you gained or lost, and by how much in percentage. Once you master a single mental model — "everything is a percentage of the cost price unless the question says otherwise" — the whole topic collapses into three or four reusable formulas. This lesson builds that model from first principles so you can solve any variation quickly and without memorising dozens of special cases.
Learning objectives
By the end of this lesson you will be able to:
- Define cost price, selling price, marked price, profit, loss, discount and commission precisely.
- Compute profit % and loss % on the correct base (almost always the cost price).
- Convert freely between CP, SP, profit%, loss%, marked price and discount%.
- Use the multiplying-factor method to chain successive percentage changes (markup then discount then tax).
- Solve the classic exam traps: false weights, two-article "sold at same price" problems, and "profit becomes loss" problems.
- Avoid the base-confusion mistakes that cost students easy marks.